One such application is to bilinear sums
with some multidimensional Salié sum which by a result of Duke [1]}
can be reduced to one dimensional sums over \(k\) -th roots (generalising the case of
\(k=2\) , see [2]}[Lemma 12.4] or [3]}[Lemma 4.4]). This result of
Duke [1]} combined with our present results and also the approach of [5]}, [6]}, [7]},
may have a potential to
lead to new asymptotic formulas for moments of \(L\) -functions with Fourier
coefficients of automorphic forms over \({\mathrm {GL}}(k)\)  with \(k \geqslant 3\) .
